49x2-1=0

The equation given is:

\[ 49x^2 - 1 = 0 \]

This is a difference of squares, which can be factored as:

\[ (7x - 1)(7x + 1) = 0 \]

Setting each factor to zero gives:

1. \( 7x - 1 = 0 \) leads to \( x = \frac{1}{7} \)
2. \( 7x + 1 = 0 \) leads to \( x = -\frac{1}{7} \)

So, the solutions are \( x = \frac{1}{7} \) and \( x = -\frac{1}{7} \).